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Dark Energy
Expanding Universe
Accelerating Universe
Dark Energy
Scott Dodelson
March 7, 2004
The Universe is Expanding
Einstein’s Equations govern
evolution of Scale Factor
Mass x Acceleration = Gravitational Force
The extent to which
expansion is speeding up
Due to the
contents of the
We can learn about the contents of the universe
by studying how the expansion varies with time
Supernovae appear fainter in an
accelerating universe
• Accelerating universe was expanding
slower in the past than non-accelerating
• Universe takes longer to get from early
scale to today in accelerating universe
• Light has more time to travel from SN at
early scale to us in accelerating universe
• SN appears fainter
Type Ia Supernovae
• Universe expanded slower
in model with Dark Energy,
so distance traveled by light
is greater: Expect fainter SN
in Dark Energy dominated
Fainter SN 
• Observed flux goes down
as distance increases. Type
Ia SN are standard candles
(i.e. have identical
luminosities), so apparent
brightness measures
Earlier times 
Acceleration is surprising
Einstein’s Equations govern
evolution of Scale Factor
Mass x Acceleration = Gravitational Force
The extent to which
expansion is speeding up
Due to the contents of the
universe: Usually it is
attractive, leading to
Einstein’s Theory of General Relativity:
Gravitational force is proportional to
Energy Density + Pressure
Accelerating universe implies
contents have negative pressure
Another View
Kinetic Energy = - Potential Energy
Expansion Rate (or the
speed of the rocket)
Decreases as rocket
gets further from
As universe expands, it should
become more dilute …
Energy density due to matter
decreases as universe expands
• Energy per particle is proportional to mass
• Number of particles in a fixed volume goes
down as the universe expands (think of
number of raisins in a fixed volume as the
bread rises)
Decrease in energy density leads
to decrease in Expansion Rate
Dark energy density must not
decrease with expansion!
Dark Energy is causing the universe
to accelerate …
What do we know about Dark
• Constitutes 2/3 of
energy in the
• Is smoothly
distributed and
Doesn’t clump into
galaxies like matter
• Has negative
Leads to
What might dark energy be and how
is it related to the rest of physics?
This is the deepest question
confronting physicists
Nothing in the Standard
Model of Particle Physics
can be the dark energy.
It might be quantum mechanical
fluctuations in the vacuum
• “Nature abhors a vacuum”
• Heisenberg’s Uncertainty Principle: even in
empty space, particles (and anti-particles)
pop in and out for short periods of time
• There is energy associated with these
quantum fluctuations …
• And they produce negative pressure!
Vacuum energy is called a
Cosmological Constant
When we calculate the energy density
associated with vacuum fluctuations …
The energy is too big by 128 orders of
We have ideas …
• The cosmological constant calculation
requires deeper understanding of quantum
• Perhaps the dark energy was not constant,
evolves in time (this has happened in the
• Perhaps dark energy is a hint of the extra
dimensions predicted by string theory
And we have plans …
Joint Dark Energy Mission
partnership to study
dark energy from
space: Launch in
Bulletin: FNAL
has just joined
the collaboration!
• The Universe is accelerating
• Dark Energy is therefore the dominant
constituent in the universe
• We do not know what dark energy is
(vacuum fluctuations? Extra dimensions?)
• We are planning missions which will tell us